Problem solving is “using existing knowledge and skills to address an unanswered question or troubling situation” (Ormrod). There are two types of problems: well-defined problems that have a clearly stated goal, information needed, and a correct solution and ill-defined problems that may not have a clear goal, all the information needed or one single solution (many possibilities may exist). Although, students are most often presented with well-defined problems in school, building skills to solve ill-defined problems is extremely important, as the real world will present these more often than a well-defined problem.
Problems are solved in one of two ways: through algorithms (a set of steps that will guarantee a correct solution) or heuristics (general strategies that may or may not lead to a successful solution). Algorithms are usually more helpful in solving well-defined problems provided that students understand how the algorithm works and when it should be used. Heuristics are especially important for ill-defined problems. Heuristics involves strategies such as breaking the problem up into smaller goals, changing complex numbers to simpler numbers, creating an analogy, and putting the problem aside for a few hours to a couple days.
Problem solving is affected by cognitive factors.
Working memory puts a limit on how much information can be thought about at one time while working through a problem.
Encoding the information into working memory in certain ways may cause a problem to be more easily or more difficultly solved. A mental set is created by repetitive practice of a certain type of problem, leading to automaticity in encoding, which can cause students to misinterpret a problem or overlook certain important aspects of the problem leading to an incorrect solution.
Metacognitive processes are also an important factor in problem solving, helping students to determine when a particular strategy should be used and allowing for flexibility in the use of problem solving strategies.
Problem Solving
Problem solving is “using existing knowledge and skills to address an unanswered question or troubling situation” (Ormrod). There are two types of problems: well-defined problems that have a clearly stated goal, information needed, and a correct solution and ill-defined problems that may not have a clear goal, all the information needed or one single solution (many possibilities may exist). Although, students are most often presented with well-defined problems in school, building skills to solve ill-defined problems is extremely important, as the real world will present these more often than a well-defined problem.
Problems are solved in one of two ways: through algorithms (a set of steps that will guarantee a correct solution) or heuristics (general strategies that may or may not lead to a successful solution). Algorithms are usually more helpful in solving well-defined problems provided that students understand how the algorithm works and when it should be used. Heuristics are especially important for ill-defined problems. Heuristics involves strategies such as breaking the problem up into smaller goals, changing complex numbers to simpler numbers, creating an analogy, and putting the problem aside for a few hours to a couple days.
Problem solving is affected by cognitive factors.
image: http://sss.usf.edu/504tutorial/Module2/CollabProbSolving.html
Kelsey Rogers